127834/1: Difference between revisions
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127834/1, the '''127834th harmonic''', or '''29-wood supermajor 119th''', is 16 octaves above [[63917/32768]]. It is a part of 397-limit harmony, the 78th prime number. | 127834/1, the '''127834th harmonic''', or '''29-wood supermajor 119th''', is 16 octaves above [[63917/32768]]. It is a part of 397-limit harmony, the 78th prime number. | ||
The number appears in a sequence of fractional part of <math>1.5^n</math> decreasing monotonically to zero, meaning the sequence offers progressively closer approximations to repeated stacks of [[3/2]]. Indeed, this interval is close to a stack of perfect fifths by two parameters - both its fractional part decreases progressively, and it is also better than all the <math>1.5^k</math> for <math>0<k<29</math>. The difference between the | The number appears in a sequence of fractional part of <math>1.5^n</math> decreasing monotonically to zero, meaning the sequence offers progressively closer approximations to repeated stacks of [[3/2]]. Indeed, this interval is close to a stack of perfect fifths by two parameters - both its fractional part decreases progressively, and it is also better than all the <math>1.5^k</math> for <math>0<k<29</math>. The difference between the stack of 29 perfect fifths and 127834/1, which is the [[68630377364883/68630356164608]] comma is 0.534 millicents, or 1 in 2.24 million parts of an octave. | ||
== Equal divisions of the 127834/1 == | == Equal divisions of the 127834/1 == | ||
Revision as of 15:17, 4 April 2023
| Interval information |
29-wood major 119th
127834/1, the 127834th harmonic, or 29-wood supermajor 119th, is 16 octaves above 63917/32768. It is a part of 397-limit harmony, the 78th prime number.
The number appears in a sequence of fractional part of [math]\displaystyle{ 1.5^n }[/math] decreasing monotonically to zero, meaning the sequence offers progressively closer approximations to repeated stacks of 3/2. Indeed, this interval is close to a stack of perfect fifths by two parameters - both its fractional part decreases progressively, and it is also better than all the [math]\displaystyle{ 1.5^k }[/math] for [math]\displaystyle{ 0\lt k\lt 29 }[/math]. The difference between the stack of 29 perfect fifths and 127834/1, which is the 68630377364883/68630356164608 comma is 0.534 millicents, or 1 in 2.24 million parts of an octave.
Equal divisions of the 127834/1
For practical purposes, 127834/1 is too complex and too large to be used as an equivalence interval, being over 100 times larger than the human hearing range.
- 29ed127834 - corresponds to Pythagorean tuning
- 261ed127834 - equivalent to Carlos Alpha
- 348ed127834 - equivalent to 12edo
Trivia
Prime numbers 23 and 397, having indices 9 and 78, are 69 prime numbers apart. Nice.